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Global bifurcation of solutions for a predator-prey model with prey-taxis. (English) Zbl 1307.92333
Summary: We study pattern formations in a predator-prey model with prey-taxis. It is proved that a branch of nonconstant solutions can bifurcate from the positive equilibrium only when the chemotactic is repulsive. Furthermore, we find the stable bifurcating solutions near the bifurcation point under suitable conditions.

MSC:
92D25 Population dynamics (general)
35K57 Reaction-diffusion equations
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